In the field of geotechnical engineering, instruments called inclinometers are available for measuring tilt in vertical or horizontal boreholes, for the purpose of calculating a path of the borehole based on one- or two-degree-of-freedom tilts, the length of the inclinometer, and the known orientation of the inclinometer about its long axis, which is controlled by straight grooves in the inclinometer casing lining the borehole. The inclinometer is either moved along the casing and stopped at spatial intervals for reading tilt (traversing inclinometer), or multiple inclinometers rest in the casing and are read at intervals in time (in-place inclinometers). Traversing inclinometers and in-place inclinometers will be referred to here as “conventional inclinometers”.
An improvement over in-place inclinometers has been patented (Danisch '363). It is a calibrated measurement instrument comprised of rigid tubes (rigid bodies) fitted with tilt sensors, the tubes separated by built-in bendable joints resistant to twist, that can be used directly without grooved casing to measure path shape and vibration along the path. Danisch '363 will be referred to hereinafter as “SAA”, or ShapeAccelArray. The SAA does not require grooves in the casing to perform azimuthal alignment of each rigid body about the long axis of the SAA. The twist-resistant joints maintain azimuthal alignment. Azimuth of each rigid body, which is not physically controlled during manufacture, is calibrated at the end of the manufacturing process, by using the X and Y tilt sensors in each body to measure the “roll” angle of each body when the SAA is generally horizontal. During manufacture, all offsets and gains of the sensors are calibrated so that accurate tilt measurements can be made over a wide temperature range, and over all angles.
Both conventional inclinometers and SAA rely on gravimetric measurement of tilt. Measurement of tilt amounts to determining the portion of the gravity vector acting upon a mass supported by springs in a reference frame, as the axis of the reference frame is tilted. In some cases, conventional inclinometers use liquid-filled curved tubes instead of springs and masses. In other cases, servo-controlled springs and masses are used.
Another prior-art measurement system similar to inclinometers is the “Bassett Convergence System”. It is an array of arms (metal rods) that form an arc around the circumference of a tunnel, all in the plane of a cross section. Angles between the arms are measured with levered tilt sensors, the levers providing amplification of the movement and conformability to a changing shape of the cross section. The angle measurements are for one degree of freedom. Convergence is the movement of the tunnel wall toward or away from the center of the tunnel. A similar measurement is made by SAA arranged within a tube formed into a circular arc and attached to the inner wall of the tunnel, also in the plane of the cross section. Angular deformation of the arc is measured in one degree of freedom and is used to measure planar convergence as in the Bassett Convergence System.
Deficiencies of both conventional inclinometers and SAA include:                Inability of the system to compress or expand axially along the path, or to measure axial deformation of the media near the instrument, such as the compression of subsiding soil, or the expansion of swelling soil. This is because the paths are nominally straight. For instance, soil compressing around an inclinometer casing will not change the length of the casing or the tilts of the instruments inside. In some cases, telescoping casing is used to enable shortening or lengthening of the casing as soil compression varies, but the tilts remain unchanged; that is the intention. Other instrumentation is needed to measure the compression of the casing or soil. Even the SAA, which can be installed in very flexible casing but is installed straight, will not be affected by soil compressing or extending around the casing, except in cases of very large lateral deformation (e.g. from a landslide), which can result in some changes in the vertical component of displacement from end-to-end of the path due to a large lateral shear at one axial location. But even when lateral deformation occurs, the axial deformation, if any, cannot be distinguished from the lateral deformation. Only if the lateral deformation were known to occur first, and then be known to be followed by pure axial compression or extension, would one be able to measure the total axial component with any confidence. However, such sequences of purely lateral and axial movements are not known to occur, and are hypothetical. Even if they did occur, no detail of axial deformation at different elevations along the path would be provided. The Bassett Convergence System allows for some expansion along its curved arc, but does not measure this expansion, nor do tunnels generally change their circumference; they generally change shape while maintaining a constant arc length.        Inability to measure lateral deformation of the path when the path is near-horizontal. This is because any rotation of a gravimetric instrument about the gravity vector does not change the influence of gravity on the instrument.        Inability to measure the shape of a surface with one instrument. Most prior-art inclinometer and SAA instruments measure deformation of an initially straight line. Multiple straight-line instruments would be required to define the shape of a surface.        Inability to measure detail of axial deformation at different locations along or near the path. This is a consequence of not measuring any axial deformation at all, or in the hypothetical case cited above, of SAA undergoing pure lateral deformation first, followed by pure axial deformation, wherein there would be no detail of axial deformation along the path; solely one axial deformation number for one lateral deformation feature (such as a shear at one axial location).        Inability to measure other than deformation within the vertical plane of an arcuate path of a convergence measurement such as an SAA in an arc, or the arc of a Bassett Convergence System. Convergence measurements are limited to movements toward or away from the center of a tunnel, performed by tilt or angle sensors arranged in an arc or circle. No measurement is made of deformation in directions out of the plane of the arc or circle.        Inability to secure the measurement instruments within a casing or tube. Instruments in boreholes and other narrow passages must be able to pass freely into the passage, yet establish secure contact with the walls of the passage when measurements are made. For SAA, this is done using joints that swell when under axial compression, but the range of swelling is only sufficient to partly stabilize the contact. For inclinometers, spring-loaded wheels are used to engage in grooves in casing, but these can become worn and are expensive to manufacture and difficult to handle. Other fastening methods are available, such as inflatable bladders, but these are expensive and complicated.        
Prior-art descriptions of conventional inclinometers and SAA are restricted to generally initially-straight paths, and do not anticipate or allow for calculations of extension and compression (either total, or in detail along the path) and lateral deformation resulting from geometries that result in changes in the straight-line separation between the ends of a purposely non-straight path. Nor does the prior art of SAA and inclinometers contemplate installation along a generally horizontal medial axis wherein is provided measurement of lateral deformation of the medial axis within a horizontal plane. By medial axis, it is meant a line or curve aligned axially with the longest dimension of a surface containing the path of an inclinometer or SAA. It follows the “center” of the path. For a straight path, it is the path. For a sinuated path, the medial axis falls between roughly equal amounts of sinuations. The medial axis will be defined more carefully later in this description.
Prior-art SAA and inclinometer descriptions are limited to generally vertical, slanted, or horizontal straight-path shapes, wherein extension or compression of the path is not possible, and measurement of lateral deformation of horizontal paths in the horizontal plane is not possible. The exception is convergence measurements performed by circles or arcs of one degree of freedom (1DOF) sensors in a vertical plane. However, these arcuate measurements are limited to movements within the plane and are either difficult to physically fit to the surface (Bassett Convergence System), or are an imperfect fit (SAA in an arcuate or circular shape within a plastic tube). The imperfect fit of the SAA will be elucidated later in this description.
In the prior art, SAA is installed by placing it in a straight tube and causing the joints to swell under axial compression, to touch the inside surface of the tube. This helps to stabilize the SAA within the tube, but is not sufficient to prevent all movement. The joints must be short enough to reduce twist, yet the shortness limits the degree to which they can swell under axial load. The swelling must diminish during insertion into or extraction from a tube, so the joints must be flexible enough to do this while still having enough stiffness to hold the array steady within the tube when swollen. The result is a compromise resulting in imperfectly-secured arrays.
In the field of geotechnical engineering there is a need to measure deformation of soils that exhibit deformation due to extension or compression, accompanied in some cases also by lateral deformation due to shearing of a layer or layers of soil, such as in an unstable slope or landslide. Compression of soils is usually associated with presence of compressible media, such as peat, within the soil, or presence of voids. Extension can result from presence of swelling clays or swelling chemical compounds present in the soil, or from injection of grout intended to stabilize weak soils. For simplicity of wording, the term “extension” (or “compression”), unless otherwise qualified, will be used to cover both cases, since extension or compression can be positive or negative (we can think of negative extension being a compression). Extension can be measured using magnets fixed to the soil next to a borehole, and a magnetic sensor moved along a borehole in the soil, but this measurement does not provide data on lateral deformation, and requires manual movement of the sensor.
In the field of geotechnical engineering there is a need to measure lateral deformation at the toe of a slope, where shearing action from above can lead to spreading of soil laterally near the bottom (“toe”) of the slope. If an SAA or conventional inclinometer is installed horizontally at the toe of a slope, it will provide measurement of deformation within a vertical plane but not a horizontal plane. This is because rotation of gravimetric devices within a horizontal plane is not sensed due to symmetry of the gravity field about the vertical dimension. Multiple vertical SAAs or conventional inclinometers can be installed to provide data on deformation within horizontal planes, but this is expensive.
In the field of tunnel and wall measurements, an installation of conventional inclinometers or SAA arrayed in a generally horizontal path along a tunnel or wall will not measure lateral deformation, because rotation of gravimetric devices within a horizontal plane is not sensed due to symmetry of the gravity field about the vertical dimension. For instance, if the wall bulges out, or if the tunnel wall curves within the horizontal plane due to excavation or grout injection nearby, the component of the bulge or curve within the horizontal plane will not be measured by the above horizontally-placed instruments. Multiple vertical conventional inclinometers or SAA may be installed, each extending from non-moving soil well below the tunnel or wall, but this solution is expensive and difficult to install.
Also in the field of tunnel measurements, it is known to place conventional inclinometers or SAA in horizontal paths along the roof, floor, or wall of a tunnel, providing measurement of deformation within vertical planes but never horizontal planes. It is also known to place such instruments in a generally circular path around the circumference, or part of the circumference, of a vertical cross section of the tunnel, for measuring convergence, which is comprised of movements of the tunnel walls toward or away from the center of the tunnel at any angle in the vertical plane. But there exists no device and method for measuring three-dimensional (3D) shape of the tunnel using a single gravity-based instrument having a single path, where “3D” implies vertical subsidence, horizontal curvature, and convergence. An analogy would be measuring all the movements of a snake including horizontal and vertical sinuation, and shape of its cross sections.
More specifically, in the field of convergence measurements introduced above, measurements in the prior art are always within the plane of the arc of the instrument. There exists a need for the single instrument to provide data not only within the plane, but extending out from the plane and including 3D aspects of the tunnel associated with movements axially along the tunnel.
In the field of geotechnical engineering there is a need to measure deformation within a vertical plane, using an installation of conventional inclinometers or SAA arrayed in a generally horizontal path, wherein extension is allowed, curving of part of the instrument up or down within the plane (e.g. heaving or subsidence) is allowed, and lateral movement is allowed, and all parameters are measured. For example, it is desirable to install inclinometers or SAA next to railway tracks to detect changes in the ballast supporting the sleepers and tracks, or along the shoulder of a road to detect erosion of the shoulder. A limitation of horizontal straight-line instruments is that if ballast or shoulder material is removed from below the path, such as by erosion or subsidence, the path of the instrument can remain unbent because the instrument is inextensible and held in tension at both edges of an area of subsidence. Thus, subsidence can occur and not be measured, or be measured with great attenuation of the depth.
In the field of geotechnical engineering there is a need to secure inclinometers or SAA so that they do not move within a casing, causing errors in tilt measurement or vibration measurement.
Conventional inclinometers are typically installed in grooved casing, with wheels engaged in the grooves to provide azimuth control and consistent registration of the inclinometer body with the walls of the casing. SAA is typically installed in un-grooved casing. SAAs have torsion-resisting joints and have been calibrated to provide a consistent azimuth along the SAA. The diameter of the casing and the length and diameter of the rigid bodies of inclinometers or SAAs set an upper limit on the amount the casing can bend without disturbing the measurements. The disturbance can result from bending of the rigid bodies, or inability of the instruments to be moved along the casing during measurement, installation, or withdrawal. This is a serious problem when large deformations are present, or for installations in rock, where bends of the casing can be very sharp and abrupt. It is generally desired to install larger-diameter casing and use shorter rigid bodies in such situations, but this leads to greater expense and loose-fitting instruments. A means of conforming a small-diameter instrument to the inside of a larger-diameter cylinder without added fixturing and without swelling joints is not described in the prior art.
Prior-art inventions have included non-straight sensor paths, but have relied on bend and twist sensors (“curvature” sensors). For instance Danisch '107 (Shape Rope”) describes                “A measuring device for providing data corresponding to a geometric configuration in space, in the form of a flexible, compliant, measurement member capable of bending in at least one degree of freedom and extending along a medial axis or plane. The member has spaced flexure sensors distributed at known locations on the member and separated by known sensor spacing intervals to provide flexure signals indicating the local state of flexure present at the locations. The member comprises a multiplicity of formed, i.e. shaped, fibers, these fibers including sensing fibers having sensing portions which provide the flexure sensors, the sensing portions of different fibers being located at differing distances along the member so as to be located at the sensor spacing intervals, the formed fibers being in mutually supporting relationship, as by continuous or repeated contact with each other. Such fibers may constitute most or all of the member”.        
Devices using flexural sensors in concatenated arrays suffer from a serious deficiency: when there is an error in one of the sensors, the orientation of all of the array past that point in the order of calculation will share the angular offset of the error, which will cause the entire data set representing a measured path to swing well away from the path, by the angle of the error. This can result in a huge displacement at the end of the path.
Further, in Danisch '107 the fibers are pre-formed and in a mutually-supporting relationship that is not suited to being compressed axially and thereby swelling laterally to conform to an enclosing surface. In fact, Danisch '107 proposes using separate extension sensors for an elastomeric form of Shape Rope that can be stretched. Danisch '107 does not teach a straight array that may be rolled up onto a reel that can be deployed straight, and then formed into a helix by inserting it into a borehole and applying axial compressive force. Instead, Danisch '107 requires that a multiplicity of fibers be pre-formed into mutually-supporting helices of fixed dimensions, the configuration not being amenable to the use of gravitational sensors measuring tilt. There is no teaching of rigid bodies separated by flexible joints, the rigid bodies providing a means of sampling tilt uniformly along a region, referenced to gravity, rather than sampling bend along a flexible member easily distorted by contact with objects. There is no teaching of flexible joints providing torsional stiffness but allowing bend, between rigid bodies. There is no teaching of referencing all the sensors to gravity, so that orientation errors cannot propagate up a calculation chain. There is no teaching of sensors in rigid bodies so that orientation may be read directly by gravimetric sensors, rather than inferred from measurements of bend and twist. There is teaching of forming the fiber optic or capacitive-fiber array, itself already in helical rope form, into helical forms, but that is no more distinguished from prior art than forming a spring or building a spiral staircase. The teaching is a description of forms that can be taken on by a flexible member, as a result of its internal cyclical structure.
The present invention incorporates helical, sinuated, and zigzag forms (cyclical forms) into a means of measuring specific new parameters, while improving the fit of the sensor array to that which is measured; but that is not all. A primary inventive step is utilizing MEMS (micro-mechanical electro-mechanical systems) accelerometers to make the measurements, even though it would seem impossible to do so, because of their limitations of orientation range, due to the directionality of gravity.
Bend and twist sensors can easily measure flexing in 3D of a rope-like structure no matter what its overall orientation might be; whereas static accelerometer measurements (“tilt” measurements or “gravimetric” measurements) could previously only be used to make 3D measurements if the overall orientation was within approximately +/−60 degrees of vertical. This is because neither X, Y, nor Z sensors respond at all to rotations about the gravity vector, and X an Y sensors (those with a maximal response to tilt when an SAA is vertical) drop in response as the cosine of the angle from vertical. Before the present invention, the only way to accomplish 3D measurement of a vertical plane was to install multiple vertical SAAs along the plane, each one extending into unmoving soil for a reference, so that each provided 3D data from a fixed reference. There was no way to extend an SAA or inclinometer along a horizontal ditch and capture movements within the horizontal plane. It was also thought impossible to couple soil subsidence movements to a thin, straight, sensor array. Once helical forms of SAA were considered, it still seemed impossible to couple that form to soil subsidence movements, until the relationship between Poisson's ratio and the helix strain ratio was recognized (this relationship is explained in detail later in this description). Advances in miniaturization of sensors, and construction methods for joints have now made it possible to contemplate the low pitch angles necessary to match the two ratios.
Although 3D measurements can be made with bend and twist sensors over a full spherical range of orientations, the accuracy of bend and twist sensors excludes them from use for monitoring geotechnical parameters. Geotechnical measurements must be accurate to one or two millimeters over array lengths of tens of meters, for decades. Practical, low-cost bend and twist sensors, such as the fiber optic curvature sensors used in the Danisch '107 and '672 prior art, are not capable of such accuracy. They are capable of approximately 1 cm per meter, per day, which is orders of magnitude too poor for geotechnical measurements.
The adaptation of cyclical forms for use with gravimetric sensors measuring at a point rather than optical or capacitive sensors integrating curvature over a path length requires the introduction of rigid bodies to contain the “point” sensors, the rigid bodies being long enough compared to the joint lengths to properly represent the tilts of the array. Practical sensing means also require design of the joints so they can be as long as possible, without requiring expensive mechanisms. The concept of long joints with monotonic and constant bend and/or twist enables much longer joints, if used so the constancy can be maintained.
Improved 2D data can also be obtained with the present invention. Straight arrays laid horizontally in a ditch can miss subsidence, such as from a washout of all the material below the array, because they are inextensible and will simply traverse the washout without appreciable sagging. A sinuated array will allow extension and make the measurement, which is very useful even if only a 2D measurement is made with just the Z sensors. Improved convergence measurements can be made by sinuating an array around its generally circular path around the circumference of a tunnel, in situations where only 2D convergence measurements within the plane of the circle are required. In this convergence case, the improvement comes from the array being better-secured within a sinuated casing, and the addition of extensibility to the circular path. Measurement of cant and twist of railway tracks is another 2D (arguably with 3D aspects) example of the improvements conferred by cyclical deployment, as are other sinuations of arrays within a horizontal plane for measuring subsidence profiles of a horizontal surface.
Similar remarks as those for Danisch '107 apply to Danisch '672 (“Shape Tape”), which describes                “A position, orientation, shape and motion measuring tool is provided in the form of a flexible substrate with bend and twist sensors distributed along its surface at known intervals. A ribbon-type substrate is preferred. The geometric configuration of the substrate is calculated from inter-referencing the locations and orientations of the sensors based upon the detected bend and twist values. Suitable applications include motion capture for humans for use in animation, six degree of freedom input to a computer, profile measurement and location tracking within a large, singularity-free working space”.        
Danisch '672 does not teach use of gravimetric sensors in rigid bodies for measuring orientations of the rigid bodies directly. Instead, it teaches measuring bend and twist along a ribbon substrate. If any bend or twist measurement is incorrect along the calculation path, then all subsequent orientations of the path, as represented by the data, will be incorrect. Danisch '672, like Danisch '107, does not teach a straight array that may be rolled up onto a reel that can be deployed straight, and then formed into a helix by inserting it into a borehole and applying axial compressive force.
Neither Danisch '672 nor '107 teaches deploying a sensor array into a surface with the form of the array and the orientations of the sensors in rigid bodies designed to exploit the use of gravitational sensors to obtain 3D data from the surface. Nor do Danisch '672 or '107 teach calculating an extensible/compressible medial axis from the forms of an array, in order to emulate the shape of an extensible/compressible virtual array in a path following the medial axis of each array. Nor do they teach tracking of vertex information in detail along a medial axis, so that compression and extension may be known in detail along the axis. Nor do '672 nor '107 teach the securing of an array within a surface by means of lateral expansion caused by axial compression of the form of the array.
One of the reasons that prior-art gravimetric arrays like Danisch '363 (SAA), and traditional in-place inclinometers have not been designed as extensible helixes or sinuated forms, and have been excluded from measuring lateral deformation from near-horizontal deployments, has been the novelty of Danisch '363. Prior to '363, it had not been considered possible to work over a wide range of angles even though relying on gravimetric sensors. Because inclinometers must be installed in grooved casing with very limited ability to bend, shapes other than straight or slightly curved could not be contemplated. Because thinking in the geotechnical field was limited to straight-path geometries, it was considered impossible to measure lateral deformation from a horizontal path, because the measured gravity field would not change for such a rotation. Danisch '363 was similarly limited in scope, disclosing only installations in straight paths that are near-horizontal or near-vertical. Near-horizontal straight paths would only yield 2D measurements. It was not until '363 was deployed in the field and had been able, due to its flexibility and wide angular range of its sensors, to measure deformations much larger than those possible with traditional inclinometers, that it was realized that it could be installed in and optimized for purposely cyclical formats that would enable new, previously impossible measurements. The present invention describes how to realize multi-dimensional measurements using new forms of SAA, even measurements that involve lateral deformation of a generally horizontal path within a vertical gravity field. It also includes descriptions of simultaneous measurement of lateral deformation and axial compression of a generally vertical path, using an inextensible array of rigid bodies fitted only with gravitational sensors.
Other improvements of the present invention over Danisch '363 (SAA) include better securing of the array in a casing, due to exploitation of helixes and sinuation. Prior-art Danisch '363 uses joints that expand under axial compression, but that leaves approximately +1-1 mm of possible movement after installation. A helical fit permits reducing this range of possible variation to essentially zero mm. A similarly tight fit can be achieved in convergence installations, for any radius of tunnel, by sinuating the path of the SAA as it travels around the circumference of the tunnel. Other improvements include being able to use wider rigid-body separations in some installations, leading to lower cost due to a reduction in the number of sensors required.